Strategic competence for multistep fraction word problems: an overlooked aspect of mathematical knowledge for teaching

Abstract

Prior work on teachers’ mathematical knowledge has contributed to our understanding of the important role of teachers’ knowledge in teaching and learning. However, one aspect of teachers’ mathematical knowledge has received little attention: strategic competence for word problems. Adapting from one of the most comprehensive characterizations of mathematics learning (NRC, 2001), we argue that teachers’ mathematical knowledge also includes strategic competence, which consists of devising a valid solution strategy, mathematizing the problem (i.e., choosing particular strategies and presentations to translate the word problem into mathematical expressions), and arriving at a correct answer (executing a solution) for a word problem. By examining the responses of 350 fourth- and fifth-grade teachers in the USA to four multistep fraction word problems, we were able to explore manifestations of teachers’ strategic competence for word problems. Findings indicate that teachers’ strategic competence was closely related to whether they devised a valid strategy. Further, how teachers dealt with known and unknown quantities in their mathematization of word problems was an important indicator of their strategic competence. Teachers with strong strategic competence used algebraic notations or pictorial representations and dealt with unknown quantities more frequently in their solution methods than did teachers with weak strategic competence. The results of this study provide evidence for the critical nature of strategic competence as another dimension needed to understand and describe teachers’ mathematical knowledge.

Preservice Elementary Teachers’ Mathematical Knowledge on Fractions as Operator in Word Problems

“…This fact has led to the need to delve into this issue by analyzing the type of instruction that students receive from teachers and the development of their competence in problem solving [48]. Likewise, it has been decided to deepen the mathematical knowledge that preservice and in-service primary teachers possess regarding the strategies for solving fraction problems [49][50][51][52], because teachers tend to replicate the strategies they have learned in their specific learning experience [53].…”

“…By examining the answers of 350 fourth-and fifth-grade teachers in the U.S.A. about their mathematical knowledge of strategic competence for multistep fraction word problems, Copur-Gencturk and Doleck [53] provided evidence for the role that strategic competence played in solving word problems, in order to understand and describe teachers' mathematical knowledge. The authors established three indicators to define the strategic competence to solve problems consisting of elaborating a solution strategy, modeling the problem and getting to the correct answer [53]. As part of capturing the teachers' strategic competence, the errors were also coded according to the relationship between them.…”

“…Subsequently, we carried out a content analysis of the written answers to identify error categories and classify the participants' answers into those categories. On the basis of recent studies [53] and through a cyclical and inductive process, the error categories defined below were refined. The three authors coded separately the errors reaching total agreement among them.…”

Research on Mathematics Problem Solving in Elementary Education Conducted from 1969 to 2021: A Bibliometric Review

“…Empirical studies on problem solving have been conducted widely in the past. These studies were conducted to identify pupils' problem solving difficulties (Tambychik & Meerah, 2010), and to determine the factors that affect pupils' problem solving ability (Herbert & Williams, 2021;Öztürk et al, 2020;Passolunghi et al, 2019;Vondrova, 2020), examine the problem solving teaching and learning process (Copur-Gencturk & Doleck, 2021;Csíkos & Szitányi, 2020;Masingila et al, 2018), and evaluate the problem solving interventions (Asigigan & Samur,2021;Goulet-Lyle et al, 2020;Lee, 2017).…”

“…The pupils are expected to master arithmetic first before any other mathematical branches such as algebra and geometry (Somasundram, 2017). Thus, majority of elementary mathematics problem solving studies are based on arithmetic and representations (Copur-Gencturk & Doleck, 2021;Pongsakdi et al, 2020). As advocated by Verschaffel et al (2007), the elementary students' institutive mathematics idea emerges when they actively constructed the knowledge using manipulatives such as based-10 blocks.…”